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We consider the sub-sector of the $c=0$ logarithmic conformal field theory(LCFT) generated by the boundary condition changing (bcc) operator in twodimensional critical percolation. This operator is the zero weight Kac operator$\phi_{1,2}$, identified with the growing hull of the SLE$_6$ process.  We identify percolation configurations with the significant operators in thetheory. We consider operators from the first four bcc operator fusions: theidentity and bcc operator; the stress tensor and its logarithmic partner; thederivative of the bcc operator and its logarithmic partner; and thepre-logarithmic operator $\phi_{1,3}$.  We construct several intervals in the percolation model, each associated toone of the LCFT operators we consider, allowing us to calculate crossingprobabilities and expectation values of crossing cluster numbers. We review theCoulomb gas, which we use as a method of calculating these quantities when thenumber of bcc operator makes a direct solution to the system of differentialequations intractable.  Finally we discuss the case of the six-point correlation function, whichapplies to crossing probabilities between the sides of a conformal hexagon.Specifically we introduce an integral result that allows one to identify theprobability that a single percolation cluster touches three alternating sides ahexagon with free boundaries. We give results of the numerical integration forthe case of a regular hexagon.

Logarithmic operator intervals in the boundary theory of critical percolation